Fractal Dimensions of the Hydrodynamic Modes of Diffusion

We consider the time-dependent statistical distributions of diffusive processes in relaxation to a stationary state for simple, two dimensional chaotic models based upon random walks on a line. We show that the cumulative functions of the hydrodynamic modes of diffusion form fractal curves in the complex plane, with a Hausdorff dimension larger than one. In the limit of vanishing wavenumber, we derive a simple expression of the diffusion coefficient in terms of this Hausdorff dimension and the positive Lyapunov exponent of the chaotic model.Comment: 20 pages, 6 figures, submitted to Nonlinearit

Twilight Intensity Variation of the Infrared Hydroxyl Airglow

The vibration rotation bands of the hydroxyl radical are the strongest features in the night airglow and are exceeded in intensity in the dayglow only by the infrared atmospheric bands of oxygen. The variation of intensity during evening twilight is discussed. Using a ground-based Fourier Transform Spectrometer (FTS), hydroxyl intensity measurements as early as 3 deg solar depression were made. Models of the twilight behavior show that this should be sufficient to provide measurement of the main portion of the twilight intensity change. The instrument was equipped with a liquid nitrogen-cooled germanium detector whose high sensitivity combined with the efficiency of the FTS technique permits spectra of the region 1.1 to 1.6 microns at high signal-to-noise to be obtained in two minutes. The use of a polarizer at the entrance aperture of the instrument reduces the intensity of scattered sunlight by a factor of at least ten for zenith observations

The Fractality of the Hydrodynamic Modes of Diffusion

Transport by normal diffusion can be decomposed into the so-called hydrodynamic modes which relax exponentially toward the equilibrium state. In chaotic systems with two degrees of freedom, the fine scale structure of these hydrodynamic modes is singular and fractal. We characterize them by their Hausdorff dimension which is given in terms of Ruelle's topological pressure. For long-wavelength modes, we derive a striking relation between the Hausdorff dimension, the diffusion coefficient, and the positive Lyapunov exponent of the system. This relation is tested numerically on two chaotic systems exhibiting diffusion, both periodic Lorentz gases, one with hard repulsive forces, the other with attractive, Yukawa forces. The agreement of the data with the theory is excellent

Playing Quantum Physics Jeopardy with zero-energy eigenstates

We describe an example of an exact, quantitative Jeopardy-type quantum mechanics problem. This problem type is based on the conditions in one-dimensional quantum systems that allow an energy eigenstate for the infinite square well to have zero curvature and zero energy when suitable Dirac delta functions are added. This condition and its solution are not often discussed in quantum mechanics texts and have interesting pedagogical consequences.Comment: 8 pages, 3 figures, requires graphicx and epsfig packages. Additional information, including individual files containing the Worksheet and a Worksheet template, are available at http://webphysics.davidson.edu/mjb/jeopardy

Specialization of the rostral prefrontal cortex for distinct analogy processes

Analogical reasoning is central to learning and abstract thinking. It involves using a more familiar situation (source) to make inferences about a less familiar situation (target). According to the predominant cognitive models, analogical reasoning includes 1) generation of structured mental representations and 2) mapping based on structural similarities between them. This study used functional magnetic resonance imaging to specify the role of rostral prefrontal cortex (PFC) in these distinct processes. An experimental paradigm was designed that enabled differentiation between these processes, by temporal separation of the presentation of the source and the target. Within rostral PFC, a lateral subregion was activated by analogy task both during study of the source (before the source could be compared with a target) and when the target appeared. This may suggest that this subregion supports fundamental analogy processes such as generating structured representations of stimuli but is not specific to one particular processing stage. By contrast, a dorsomedial subregion of rostral PFC showed an interaction between task (analogy vs. control) and period (more activated when the target appeared). We propose that this region is involved in comparison or mapping processes. These results add to the growing evidence for functional differentiation between rostral PFC subregions

Could a CAMELS downgrade model improve off-site surveillance?

The Federal Reserve’s off-site surveillance system includes two econometric models that are collectively known as the System for Estimating Examination Ratings (SEER). One model, the SEER risk rank model, uses the latest financial statements to estimate the probability that each Fed-supervised bank will fail in the next two years. The other component, the SEER rating model, uses the latest financial statements to produce a “shadow” CAMELS rating for each supervised bank. Banks identified as risky by either model receive closer supervisory scrutiny than other state-member banks.> Because many of the banks flagged by the SEER models have already tumbled into poor condition and, hence, would already be receiving considerable supervisory attention, we developed an alternative model to identify safe-and-sound banks that potentially are headed for financial distress. Such a model could help supervisors allocate scarce on- and off-site resources by pointing out banks not currently under scrutiny that need watching.> It is possible, however, that our alternative model improves little over the current SEER framework. All three models—the SEER risk rank model, the SEER rating model, and our downgrade model—produce ordinal rankings based on overall risk. If the financial factors that explain CAMELS downgrades differ little from the financial factors that explain failures or CAMELS ratings, then all three models will produce similar risk ratings and, hence, similar watch lists of one- and two-rated banks.> We find only slight differences in the ability of the three models to spot emerging financial distress among safe-and-sound banks. In out-of-sample tests for 1992 through 1998, the watch lists produced by the downgrade model outperform the watch lists produced by the SEER models by only a small margin. We conclude that, in relatively tranquil banking environments like the 1990s, a downgrade model adds little value in off-site surveillance. We caution, however, that a downgrade model might prove useful in more turbulent banking times.Bank supervision

Low-speed stability and control wind-tunnel investigations of effects of spanwise blowing on fighter flight characteristics at high angles of attack

The effects of spanwise blowing on two configurations representative of current fighter airplanes were investigated. The two configurations differed only in wing planform, with one incorporating a trapezoidal wing and the other a 60 delta wing. Emphasis was on determining the lateral-directional characteristics, particularly in the stall/departure angle-of-attack range; however, the effects of spanwise blowing on the longitudinal aerodynamics were also determined. The-tunnel tests included measurement of static force and forced-oscillation aerodynamic data, visualization of the airflow changes created by the spanwise blowing, and free-flight model tests. The effects of blowing rate, chordwise location of the blowing ports, asymmetric blowing, and blowing on the conventional aerodynamic control characteristics were investigated. In the angle-of-attack regions in which the spanwise blowing substantially improved the wing upper-surface flow field (i.e., provided reattachment of the flow aft of the leading-edge vortex), improvements in both static and dynamic lateral-directional stability were observed. Blowing effects on stability could be proverse or adverse depending on blowing rate, blowing port loaction, and wing planform. Free-flight model tests of the trapezoidal wing confirmed the beneficial effects of spanwise blowing measured in the static and dynamic force tests